1. Technical Field
The present application relates to an electronic state calculation method, an electronic state calculation device and a recording medium for obtaining an electronic state of a material by a calculation.
2. Description of the Related Art
Conventionally, there exits a calculation theory called a first-principle calculation theory of estimating physical or chemical properties of a material (hereinafter, referred to as properties) according to a basic rule of quantum mechanics. Of this calculation theory, a calculation theory based on a density functional theory is present in which properties such as mechanical properties including elasticity, conductive properties including superconductive properties, a dielectric property, and a magnetic property are approximately reproduced and the calculation scale is within an implementable range. This calculation theory has already been applied to material design, and there exist a multiplicity of examples with its expectation accuracy and accuracy limit verified through experiments.
Although the calculation theory based on the density functional theory includes a self-consistent calculation theory by local density approximation (LDA), it is known that the calculation result does not always show the same properties as in experiments.
As calculation techniques based on the density functional theory, a plurality of approximate calculation techniques are known such as generalized-gradient approximation (GGA), GW approximation, GW+Γ approximation and LDA+U approximation positioned as techniques to overcome a problem with the LDA, and regarding these approximate calculation techniques, it is also known that the calculation result does not always show the same properties as in experiments.
The above-mentioned approximate calculation techniques all have a problem that they do not provide a method for always attaining the properties shown by a real solution (exact solution) by a finite number of times of calculation. That is, no self-consistent calculation theory is present that always ensures reproduction of the properties of the real solution while utilizing a high-accuracy one-electron basis provided by the LDA.
On the other hand, one of the inventors of the present application has proposed a fluctuation reference determination method as an effective many-electron calculation based on a multi-reference density functional method. By this method, the reproduction accuracy of the physical quantities can be improved with a given accuracy by providing an extended Kohn-Sham equation to reproduce a fluctuation variable (correlation function) having a positive definite property such as local density fluctuations in addition to the one-electron density. According to this calculation technique, the total energy, the one-electron density and the specified fluctuation variable of a material are simultaneously reproduced through the determination of the minimum energy state of a Hamiltonian. Further, by using, as the initial values, a model determined by the extended Kohn-Sham equation and its stability solution, a time development equation to reproduce the total energy, the one-electron density and the canonical correlation function is provided, and a high-accuracy first-principle electron state calculation method for reproducing external field responses (such as responses to dynamic deformation and electric field application) of the material is provided.
However, the effective many-electron calculation based on the multi-reference density functional method is a calculation technique for which a reference calculation such as a quantum Monte Carlo method, a transcorrelated method, a configuration interaction method, a perturbational calculation/Green's function method or an effective potential method is inevitable. For this reason, the reproduction accuracy of the physical quantities depends on the calculation accuracy of the reference calculation, and a calculation technique by which the real solution is attained beyond the calculation accuracy of the reference calculation is not provided.
Accordingly, one of the inventors of the present application has further proposed an electronic state calculation method, an electronic state calculation device, a computer program and a recording medium by which exact solution evaluation can be performed by providing a quantum-mechanical variation calculation theory using a density functional (density functional variational method) and a method that provides an approximation model sequence attaining the exact solution in a model space as a Banach space containing the exact solution, and obtaining a stable numerical solution within a range permitted by the calculator resources.
However, when the goal is limited to reproduction of only the physical or chemical properties of a material, the method that attains the exact solution by an approximation model sequence attaining the exact solution in the model space does not use the attainment of the properties of the exact solution by a smaller finite number of times of calculation.